The zero temperature Hall constant R H , described by reactive (nondissipative) conductivities, is analyzed within linear response theory. It is found that in a certain limit R H is directly related to the density dependence of the Drude weight, implying a simple picture for the change of sign of charge carriers in the vicinity of a Mott-Hubbard transition. This novel formulation is applied to the calculation of R H in quasi-one-dimensional and ladder prototype interacting electron systems. PACS numbers: 71.27. + a, 71.10.Fd, 72.15.Gd It is now well known that in strongly correlated systems, zero temperature (T 0), the reactive part of the conductivity can be used as a criterion of a metallic or insulating ground state [1]. In particular, following the work of Kohn, the imaginary part of the conductivity, s 00 ͑v ! 0͒ 2D͞v, characterized by D (now called the "Drude weight" or charge stiffness), can be related to the ground state energy density e 0 dependence on an applied fictitious flux f as D ͑1͞2͒≠ 2 e 0 ͞≠f 2 j f!0 .A similar question is posed by the doping of an insulating state, where it would be interesting to have a simple description of the charge carriers sign as probed in a Hall experiment. For instance, we would like to describe the doping of a Mott-Hubbard insulator; within a semiclassical approach it is expected that the Hall constant R H Ӎ 11͞ed, holelike (positive) near half filling (d 1 2 n, n density), changing to R H Ӎ 21͞en, electronlike at low densities, the turning point depending on the interaction.Over the recent years, ingenious ways have been proposed [2,3] for characterizing this sign change and strongly correlated electron systems, such as the t-J model, have been studied. In particular, following the suggestion to focus on the T 0 Hall constant within linear response theory [4], the R H of a hole in the t-J model was analyzed and a numerical method was proposed for calculating the Hall response in ladder systems [5]. This activity is partly motivated by the physics of high temperature superconductors viewed as doped Mott-Hubbard insulators and related Hall measurements showing a change of the sign of carriers with doping [6].In this Letter, we show that within a certain frequency v, wave vector q limiting procedure, the T 0, v ! 0, thus "reactive" Hall constant, is simply related to the density dependence of the Drude weight. Following this point of view, we recover in a straightforward way: (i) the semiclassical expressions for R H at low density and near an insulating state, (ii) a physical picture of the sign change of carriers in the vicinity of a Mott-Hubbard transition and its dependence on interaction strength, (iii) a common expression used to describe the Hall constant in quasi-onedimensional conductors described by a band picture [7], (iv) good accord with R H for ladder systems calculated using the numerical method proposed in [5].The Hamiltonian.-In the following we will consider a generic Hamiltonian for fermions on a lattice, where for simplicity we describe the kinet...